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Stochastic Target Approach to Ricci Flow on surfaces

Series:

Stochastics Seminar

Thursday, September 27, 2012 - 15:05

1 hour (actually 50 minutes)

Location:

Skiles 006

Speaker:

Ionel Popescu

,

School of Mathematics, Georgia Tech

Ricci flow is a sort of (nonlinear) heat problem under which the metric on a given manifold is evolving. There is a deep connection between probability and heat equation. We try to setup a probabilistic approach in the framework of a stochastic target problem. A major result in the Ricci flow is that the normalized flow (the one in which the area is preserved) exists for all positive times and it converges to a metric of constant curvature. We reprove this convergence result in the case of surfaces of non-positive Euler characteristic using coupling ideas from probability. At certain point we need to estimate the second derivative of the Ricci flow and for that we introduce a coupling of three particles. This is joint work with Rob Neel.